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Re: What is the purpose of the Defer Command?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg82083] Re: What is the purpose of the Defer Command?
  • From: Chris Chiasson <chris.chiasson at gmail.com>
  • Date: Thu, 11 Oct 2007 00:26:38 -0400 (EDT)
  • References: <fe4uhp$155$1@smc.vnet.net><fei1u1$pmv$1@smc.vnet.net>

On Oct 10, 3:19 am, Chris  Chiasson <chris.chias... at gmail.com> wrote:
> On Oct 9, 4:34 am, "DavidPark" <djmp... at comcast.net> wrote:
>
>
>
> > Still, my question is: "What is the purpose of theDeferCommand?"
>
> > The only potential purpose that I can see is for didactic purposes, to show
> > preliminary expressions before they are automatically evaluated. But the
> > only way to getDeferto evaluate is by copying and pasting and then
> > evaluating,  by using Shift-Ctrl-L and then evaluating, or by evaluating in
> > place. All of these operations leave no record of the steps taken. That goes
> > contrary to any didactic purpose.
>
> > --
> > DavidPark
> > djmp... at comcast.nethttp://home.comcast.net/~djmpark/
>
> > "DavidPark" <djmp... at comcast.net> wrote in message
>
> >news:fe4uhp$155$1 at smc.vnet.net...
>
> > >I do not understand the utility of the newDeferstatement in Mathematica
> > > Version 6. Also, it seems to me to be similar to, but not as good as, the
> > > HoldTemporary command introduced by Ted Ersek on MathSource a few years
> > > ago.
>
> > > The help forDefersays: "Defer[expr] yields an object that displays as
> > > the
> > > unevaluated form of expr, but which is evaluated if it is explicitly given
> > > as Mathematica input." What does 'given as Mathematica input' mean? The
> > > examples seem to only involve copying and pasting, which I don't consider
> > > a
> > > great method for doing mathematics, or evaluation in place.
>
> > > I would like to understand howDefermight be used in expository notebooks
> > > to clarify some piece of mathematics. The problem is that it requires an
> > > interactive action, which would be invisible to a reader of a notebook.  I
> > > think the idea of 'modification in place' is poor in technical
> > > communication
> > > because it destroys the record of what was done.
>
> > > (In the examples below, whenever an output resulted in an expression that
> > > copied as a box structure, I converted to InputForm to simplify the
> > > posting.)
>
> > > Here is a simple example:
>
> > > y =Defer[1 + 1]
> > > 1 + y                                               giving
>
> > > 1 + 1
>
> > > 1 + (1 + 1)
>
> > > I would prefer that theDeferexpression would have evaluated in the
> > > second
> > > statement but I guess it is logical that it didn't. If I write:
>
> > > 1 + y
>
> > > then select the y and Evaluate In Place I obtain the following, which must
> > > then be further evaluated to obtain 3.
>
> > > 1 + 1 + 1
>
> > > 3
>
> > > A second example. I want to show an integral without evaluation and then
> > > the
> > > evaluated result. I have to write the following expression, then select
> > > the
> > > second line of output, evaluate in place, and then I obtain the result -
> > > but
> > > as an Input cell. This is certainly a place where HoldForm would be
> > > better.
>
> > >Defer[Integrate[x^2 Exp[-x], {x, 0, 1}]]
> > > %
> > > giving
>
> > > Integrate[x^2/E^x, {x, 0, 1}]
>
> > > 2 - 5/\[ExponentialE]                        (which is an Input cell)
>
> > > Here is third example.Deferdoes not evaluate and we obtain an error
> > > message.
>
> > > numb =Defer[2^67 - 1]
> > > FactorInteger[numb]                                       giving
>
> > > 2^67 - 1
>
> > > FactorInteger::"exact" :  "\"Argument \!\(\*SuperscriptBox[\"2\", \
> > > \"67\"]\) - 1 in FactorInteger[\!\(\*SuperscriptBox[\"2\", \"67\"]\) \
> > > - 1] is not an exact number\""
>
> > > FactorInteger[2^67 - 1]
>
> > > But it works if I copy and paste into FactorInteger.
>
> > > Now, look at the behavior of Ted's MathSource package.
>
> > > Needs["Enhancements`HoldTemporary`"]
>
> > > y = HoldTemporary[1 + 1]
> > > 1 + y                                                        giving
>
> > > 1 + 1
>
> > > 3
>
> > > The expression is evaluated if it is an argument of some function.
>
> > > HoldTemporary[Integrate[x^2 Exp[-x], {x, 0, 1}]]
> > > Identity[%]
> > > giving
>
> > > Integrate[x^2/E^x, {x, 0, 1}]
>
> > > 2 - 5/\[ExponentialE]       (which is an Output cell)
>
> > > numb = HoldTemporary[2^67 - 1]
> > > FactorInteger[numb]                                            giving
>
> > > 2^67 - 1
>
> > > {{193707721, 1}, {761838257287, 1}}
>
> > > Much better. I might be missing the point, but I don't think thatDeferis
> > > at all well designed.
>
> > > There is another Hold that is very useful. This is one that holds an
> > > operation but evaluates the arguments. We have a HoldOp statement in the
> > > Tensorial package.
>
> > > Needs["TensorCalculus4V6`Tensorial`"]
>
> > > ?HoldOp
>
> > > HoldOp[operation][expr] will prevent the given operation from being
> > > evaluated in expr. Nevertheless, other operations within expr will be
> > > evaluated. Operation may be a pattern, including alternatives, that
> > > represents heads of expressions. The HoldOp can be removed with
> > > ReleaseHold.
>
> > > One reason we want the arguments to evaluate is that the arguments often
> > > contain tensor shortcut expressions and we want them evaluated to show the
> > > full tensor expression inside some operation. However, there are many
> > > other
> > > uses.
>
> > > f[x_] := Sin[x] \[ExponentialE]^x
>
> > > We would like f[x] to be evaluated inside the Integrate statement, but
> > > hold
> > > the actual itegration.
>
> > > Integrate[f[x], {x, 0, \[Pi]}] // HoldOp[Integrate]
> > > % // ReleaseHold
> > > giving
>
> > > HoldForm[Integrate[E^x*Sin[x], {x, 0, Pi}]]
>
> > > 1/2 (1 + \[ExponentialE]^\[Pi])
>
> > > For exposition purposes we might want to keep the following expression in
> > > the input order.
>
> > > \[Pi]  Sin[x] \[ExponentialE]^x // HoldOp[Times]
> > > % // ReleaseHold
> > > giving
>
> > > HoldForm[Pi*Sin[x]*E^x]
>
> > > \[ExponentialE]^x \[Pi] Sin[x]
>
> > > Often we will have cases where some operation has automatic built-in
> > > rules,
> > > such as linear and Leibnizian breakouts with differentiation. Again, for
> > > exposition purposes, we might want to show the expression before these
> > > rules
> > > are applied.
>
> > > g[x_] := x^2
>
> > > D[a f[x] g[x], x] // HoldOp[D]
> > > % // ReleaseHold                                    giving
>
> > > HoldForm[D[a*E^x*x^2*Sin[x], x]]
>
> > > a \[ExponentialE]^x x^2 Cos[x] + 2 a \[ExponentialE]^x x Sin[x] +
> > > a \[ExponentialE]^x x^2 Sin[x]
>
> > > --
> > > DavidPark
> > > djmp... at comcast.net
> > >http://home.comcast.net/~djmpark/
>
> You have quite obviously missed the point. Without Defer, we might
> actually have to type ReleaseHold. Furthermore, symbols like Defer are
> only afforded by keeping the System context free of useless symbols
> such as AxesInFront and GridLinesInFront. Stick that in your pipe and
> smoke it.
>
> Sincerely,
>
> --http://chris.chiasson.name/

I have received at least one email that reprimanded me for my email
above. I feel compelled to note that the email above is a joke and
actually refers to this previous thread:

http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_thread/thread/c5d2ee609ba69bbc

It is meant to highlight changes that, from the outside, seem
capricious and wrong, while taking the sting out of the criticism -
criticism that is meant for WRI, not the esteemed Mr. Park.



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